We are given a graph of a function and asked to find the intervals where the function is increasing, decreasing, or constant, as well as the domain and range of the function.

1. Problem Description

We are given a graph of a function and asked to find the intervals where the function is increasing, decreasing, or constant, as well as the domain and range of the function.

2. Solution Steps

* Increasing Interval: The function is increasing when the y-value increases as the x-value increases. From the graph, this occurs from $x = 2$ to $x = 5$. At $x=5$ the function has a hole, so the interval is $(2, 5)$.

* Decreasing Interval: The function is decreasing when the y-value decreases as the x-value increases. From the graph, this occurs from $x = -6$ to $x = -3$. Since $-6$ is a closed circle, the interval includes $-6$. Therefore, the interval is $[-6, -3)$.

* Constant Interval: The function is constant when the y-value remains the same as the x-value increases. From the graph, this occurs from $x = -3$ to $x = 2$. Therefore, the interval is $[-3, 2]$.

* Domain: The domain is the set of all possible x-values for the function. From the graph, the function is defined from $x = -6$ to $x = 5$. Since $-6$ is a closed circle and $5$ is an open circle (hole), the domain is $[-6, 5)$.

* Range: The range is the set of all possible y-values for the function. The minimum y-value is $-2$, and the maximum y-value approaches

1. Therefore, the range is $[-2, 1)$.

3. Final Answer

* Increasing: $(2, 5)$

* Decreasing: $[-6, -3)$

* Constant: $[-3, 2]$

* Domain: $[-6, 5)$

* Range: $[-2, 1)$